Quick recall · 236 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ
Tap to reveal →
Aubrey can run at a pace of 6 miles per hour. Running at the same rate, how many miles can she run in 90 minutes?
D · 9
First convert 90 minutes to hours: \( 90 \div 60 = 1.5 \) hours.Distance = speed × time = \( 6 \times 1.5 = 9 \) miles.Option D is 9, which matches the calculated distance.
PYQ
Tap to reveal →
A number is divided by four. The result is divided by three, for a final result of two. What was the original number?
D · 24
Let original number be \( x \).After dividing by 4: \( \frac{x}{4} \).Then divide by 3: \( \frac{x}{4} \div 3 = \frac{x}{12} = 2 \).Thus, \( x = 2 \times 12 = 24 \).Option D is 24.
PYQ
Tap to reveal →
What is the difference between 3.8 and 0.571?
C · 3.229
Difference means subtraction: \( 3.8 - 0.571 \).Align decimals: \( 3.800 \) \( -0.571 \) \( 3.229 \)Option C is 3.229.
PYQ
Tap to reveal →
What is 2.567 rounded to the nearest hundredth?
C · 2.57
Hundredth place is 6, thousandth is 7 (≥5, so round up).2.56 → 2.57.Option C is 2.57.
PYQ
Tap to reveal →
Which two numbers and signs should be interchanged to make the following equation correct? 14 × 3 ÷ 6 – 12 + 13 = 8
A · A. 14 and 12, × and ÷
PYQ
Tap to reveal →
Which of the following represents \( \frac{1}{8} \) as a decimal?
A · 0.125
PYQ
Tap to reveal →
Which fraction is between 1.3 and 1.4?
A · \( 1\frac{1}{3} \)
PYQ
Tap to reveal →
Is the ratio 5:10 proportional to 1:2?
A · Yes, they are proportional
PYQ
Tap to reveal →
A classroom has 15 boys and 13 girls. If 10 more girls join the class, what is the ratio of girls to boys?
B · 23:15
PYQ
Tap to reveal →
If the average weight of the group is 68 kg, where women have an average weight of 60 kg and men have an average weight of 72 kg, what is the ratio of women to men in the group?
D · 1 : 2
PYQ
Tap to reveal →
₹2,500, when invested for 8 years at a given rate of simple interest per year, amounted to ₹3,725 on maturity. What was the rate of simple interest that was paid per annum?
C · C) 5%
PYQ
Tap to reveal →
A sum becomes Rs. 10650 in 5 years and Rs. 11076 in 6 years. What is the principal amount?
B · B) Rs. 8520
Interest for 1 year = 11076 - 10650 = Rs. 426.Interest for 5 years = 426 × 5 = 2130.Principal = Amount after 5 years - Interest for 5 years = 10650 - 2130 = Rs. 8520.This matches option B.
PYQ
Tap to reveal →
A sum of Rs. 5000 is deposited for 2 years at 5% simple interest per annum. What is the simple interest earned?
B · B) Rs. 500
Simple Interest formula: \( SI = \frac{P \times R \times T}{100} \).P = 5000, R = 5%, T = 2 years.SI = \(\frac{5000 \times 5 \times 2}{100} = 500\).∴ The correct answer is Rs. 500, option B.
PYQ
Tap to reveal →
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
C · C) Rs. 698
S.I. for 1 year = (854 - 815) = Rs. 39.S.I. for 3 years = 39 × 3 = Rs. 117.Principal = 815 - 117 = Rs. 698.This matches option C.
PYQ
Tap to reveal →
A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
C · Rs. 122
Question bank
Tap to reveal →
What is the sum of 245 and 378?
B · 623
Adding 245 and 378 gives 623.
Question bank
Tap to reveal →
Calculate the product of 16 and 25.
B · 400
16 \times 25 = 400.
Question bank
Tap to reveal →
Evaluate \( 725 - 438 \).
A · 287
725 minus 438 equals 287.
Question bank
Tap to reveal →
If \( \frac{1}{4} \) of a number is 36, what is the number?
B · 144
Let the number be x. Then \( \frac{x}{4} = 36 \) so \( x = 36 \times 4 = 144 \). Check options, 180 is incorrect; correct is 144, which corresponds to option B. Correct answer should be B.
Question bank
Tap to reveal →
A shopkeeper sold 120 items at \$15 each. If the cost price of each item is \$12, what is the total profit?
A · \$360
Profit per item = 15 - 12 = 3. Total profit = 120 \times 3 = 360.
Question bank
Tap to reveal →
Evaluate \(8 + 3 \times (12 - 4) \).
A · 32
First calculate inside the parentheses: 12 - 4 = 8. Then multiply: 3 \times 8 = 24. Finally add: 8 + 24 = 32.
Question bank
Tap to reveal →
Calculate \( (18 - 2) \div 4 + 3 \times 2 \).
A · 11
Question bank
Tap to reveal →
Evaluate \( 6 + 4 \times 3^2 - 8 \div 2 \).
A · 37
Question bank
Tap to reveal →
Simplify using distributive law: \( 5 \times (3 + 7) \).
C · 5 \times 3 + 5 \times 7
Distributive law states \( a(b + c) = ab + ac \). So, \( 5 \times (3 + 7) = 5 \times 3 + 5 \times 7 \).
Question bank
Tap to reveal →
Which of the following shows the associative property of addition?
A · \( (2 + 3) + 4 = 2 + (3 + 4) \)
Associative property of addition refers to grouping: \( (a + b) + c = a + (b + c) \).
Question bank
Tap to reveal →
If \( (a \times b) \times c = a \times (b \times c) \), which property is being used?
C · Associative property
The associative property states that the way numbers are grouped does not change the product.
Question bank
Tap to reveal →
Which of the following is true?
A · \( 4 + 5 = 5 + 4 \)
Commutative property holds for addition but not for subtraction or division.
Question bank
Tap to reveal →
Find the greatest common factor (GCF) of 36 and 54.
C · 18
Factors of 36: 1,2,3,4,6,9,12,18,36; Factors of 54:1,2,3,6,9,18,27,54; Greatest common factor is 18.
Question bank
Tap to reveal →
Which number is a multiple of both 6 and 8?
A · 24
24 is a multiple of 6 (6\times4) and 8 (8\times3).
Question bank
Tap to reveal →
What is the least common multiple (LCM) of 12 and 15?
A · 60
Multiples of 12: 12,24,36,48,60... Multiples of 15: 15,30,45,60... The least common multiple is 60.
Question bank
Tap to reveal →
If a number is divisible by both 2 and 3, it must be divisible by:
B · 6
The number must be divisible by the LCM of 2 and 3, which is 6.
Question bank
Tap to reveal →
Which of the following numbers is divisible by 3?
B · 123
Sum of digits of 123 is 1+2+3=6, which is divisible by 3, so 123 is divisible by 3.
Question bank
Tap to reveal →
According to divisibility rules, which number is divisible by 9?
A · 729
Sum of digits of 729 = 7+2+9=18 which is divisible by 9, so 729 is divisible by 9.
Question bank
Tap to reveal →
Which of these numbers is divisible by 4?
A · 1216
A number is divisible by 4 if its last two digits form a number divisible by 4. Here, 16 is divisible by 4.
Question bank
Tap to reveal →
Which number is divisible by both 3 and 5?
A · 135
Number divisible by both 3 and 5 must be divisible by 15. 135 \div 15 = 9, so 135 fits.
Question bank
Tap to reveal →
Calculate \( \frac{3}{5} + \frac{7}{10} \).
A · \( \frac{11}{10} \)
Common denominator is 10; \( \frac{3}{5} = \frac{6}{10} \). Sum = \( \frac{6}{10} + \frac{7}{10} = \frac{13}{10} = 1 \frac{3}{10} \). Revised option A to \( \frac{13}{10} \).
Question bank
Tap to reveal →
Subtract \( 2 \frac{3}{4} - 1 \frac{5}{6} \).
B · \( \frac{11}{12} \)
Question bank
Tap to reveal →
Multiply \( \frac{5}{6} \times \frac{9}{10} \).
A · \( \frac{3}{4} \)
Multiply numerators and denominators: \( \frac{5 \times 9}{6 \times 10} = \frac{45}{60} = \frac{3}{4} \).
Question bank
Tap to reveal →
Divide \( \frac{7}{8} \) by \( \frac{14}{16} \).
C · 1
Division of fractions: \( \frac{7}{8} \div \frac{14}{16} = \frac{7}{8} \times \frac{16}{14} = \frac{7 \times 16}{8 \times 14} = \frac{112}{112} = 1 \). Recalculation shows 1.
Question bank
Tap to reveal →
Convert 0.375 to a fraction in simplest form.
A · \( \frac{3}{8} \)
0.375 = \( \frac{375}{1000} \). Simplify by dividing numerator and denominator by 125: \( \frac{3}{8} \).
Question bank
Tap to reveal →
What is 25% of 240?
B · 60
25% of 240 = \( \frac{25}{100} \times 240 = 60 \).
Question bank
Tap to reveal →
Express 0.56 as a percentage.
B · 56%
Multiply decimal by 100 to get percentage: 0.56 \times 100 = 56%.
Question bank
Tap to reveal →
An item priced at \$120 is marked down by 15%. What is the sale price?
B · \$102
Discount = 15% of 120 = 18. Sale price = 120 - 18 = 102. Correct answer: \$102, option B.
Question bank
Tap to reveal →
John had 15 apples. He gave \( \frac{1}{3} \) of them to Mary and \( 20\% \) of the remaining apples to David. How many apples does John have now?
B · 8
John gave 1/3 of 15 = 5 apples to Mary.Remaining apples = 15 - 5 = 10.He gave 20% of 10 = 2 apples to David.Apples left = 10 - 2 = 8 apples, option B revised as correct.
Question bank
Tap to reveal →
A car travels 150 km in 3 hours and then 200 km in 4 hours. What is the average speed of the car for the entire journey?
C · 50 km/h
Total distance = 150 + 200 = 350 km.Total time = 3 + 4 = 7 hours.Average speed = 350/7 = 50 km/h. Correct answer: 50 km/h, option C.
Question bank
Tap to reveal →
If \( 5x + 3 = 28 \), what is the value of \( x \)?
B · 5
5x + 3 = 285x = 25x = 5
Question bank
Tap to reveal →
What is the value of \( 58 + 27 \)?
A · 85
Adding 58 and 27 yields 85 (58 + 27 = 85).
Question bank
Tap to reveal →
Calculate \( 90 - 43 \).
B · 47
Subtracting 43 from 90 gives 47 (90 - 43 = 47).
Question bank
Tap to reveal →
Find the product of 12 and 7.
B · 84
Multiplying 12 by 7 gives 84 (12 \times 7 = 84).
Question bank
Tap to reveal →
What is \( \frac{144}{12} \)?
A · 12
Dividing 144 by 12 results in 12 (144 \div 12 = 12).
Question bank
Tap to reveal →
Simplify \( 15 \times 3 - 9 \div 3 \).
C · 42
First multiply and divide: \(15 \times 3 = 45\), \(9 \div 3 = 3\). Then subtract: \(45 - 3 = 42\). Actually, the calculation is \(45 - 3 = 42\), so option C is correct.
Question bank
Tap to reveal →
Which of the following equals \( (24 - 6) \div (3 + 1) \)?
D · 4.5
First calculate inside the brackets: \(24 - 6 = 18\), \(3 + 1 = 4\). Then divide: \(18 \div 4 = 4.5\). Correct answer is D.
Question bank
Tap to reveal →
Evaluate \( 8 + 2 \times 5 \) following correct order of operations.
C · 18
According to BODMAS, multiply first: \(2 \times 5 = 10\), then add 8: \(8 + 10 = 18\).
Question bank
Tap to reveal →
Calculate \( (6 + 4) \times (9 - 3) \div 3 \).
B · 20
Calculate inside parentheses: \(6 + 4 = 10\), \(9 - 3 = 6\). Then multiply: \(10 \times 6 = 60\). Finally divide: \(60 \div 3 = 20\). Correct answer is B.
Question bank
Tap to reveal →
Simplify \( 3 + 12 \div (2 \times 2) - 1 \).
A · 5
Inside parentheses: \(2 \times 2 = 4\). Division: \(12 \div 4 = 3\). Expression becomes \(3 + 3 - 1 = 5\).
Question bank
Tap to reveal →
Which property justifies that \( 7 + 3 = 3 + 7 \)?
C · Commutative Property
The Commutative Property states that changing the order of numbers in addition or multiplication does not change the result.
Question bank
Tap to reveal →
Evaluate \( (2 + 3) + 5 \) and \( 2 + (3 + 5) \) to verify which property applies.
B · Associative Property
The Associative Property states that the way numbers are grouped in addition or multiplication does not change the sum or product.
Question bank
Tap to reveal →
Which of these expresses the Distributive Property?
B · \( a \times (b + c) = a \times b + a \times c \)
The Distributive Property states that multiplication distributes over addition as \( a \times (b + c) = a \times b + a \times c \).
Question bank
Tap to reveal →
Identify the property that explains \( (4 \times 5) \times 3 = 4 \times (5 \times 3) \).
B · Associative Property
The Associative Property refers to regrouping the numbers without changing the product or sum.
Question bank
Tap to reveal →
Simplify \( 3 \times (7 + 5) \) using distributive property.
A · 36
Using distributive property: \(3 \times 7 + 3 \times 5 = 21 + 15 = 36\).
Question bank
Tap to reveal →
Which number is a factor of 36?
B · 6
6 divides 36 exactly since \(36 \div 6 = 6\).
Question bank
Tap to reveal →
Find the least common multiple (LCM) of 4 and 6.
A · 12
Multiples of 4: 4, 8, 12,... Multiples of 6: 6, 12, 18,... Common multiple is 12, which is the smallest.
Question bank
Tap to reveal →
What is the greatest common factor (GCF) of 48 and 60?
D · 24
Factors of 48 include 24 and factors of 60 include 24; 24 is the greatest common factor.
Question bank
Tap to reveal →
Find all factors of 17.
A · 1 and 17
Since 17 is prime, its only factors are 1 and 17.
Question bank
Tap to reveal →
Which of the following numbers is prime?
B · 41
41 is a prime number because it has no divisors other than 1 and itself.
Question bank
Tap to reveal →
Is 91 a prime or composite number?
B · Composite
91 is composite because it is divisible by 7 and 13 other than 1 and 91.
Question bank
Tap to reveal →
Which of these is a composite number?
C · 33
33 is composite because it can be divided by 3 and 11 besides 1 and 33.
Question bank
Tap to reveal →
If Sarah buys 3 packs of pencils with 24 pencils in each pack, how many pencils does she buy in total?
A · 72
Total pencils = 3 \times 24 = 72.
Question bank
Tap to reveal →
A car travels 45 miles in 3 hours. How far will it travel in 7 hours at the same speed?
A · 105 miles
Speed = 45 \div 3 = 15 mph, distance = 15 \times 7 = 105 miles.
Question bank
Tap to reveal →
A shop sold 120 apples in 4 hours. If they sold the apples evenly each hour, how many apples were sold per hour?
A · 30
Apples per hour = 120 \div 4 = 30.
Question bank
Tap to reveal →
Tom has \$50. He spends \$15 on lunch and \$20 on a book. What fraction of his money remains?
A · \( \frac{3}{10} \)
Spent \$35, remaining \$15; fraction = \( \frac{15}{50} = \frac{3}{10} \) actually, so correct answer is A.
Question bank
Tap to reveal →
A factory produces 120 units in 8 hours. At this rate, how many units will it produce in 15 hours?
D · 225
Units per hour = 120 \div 8 = 15; units in 15 hours = 15 \times 15 = 225.
Question bank
Tap to reveal →
Which number is divisible by 9?
A · 234
Sum of digits in 234 is 2 + 3 + 4 = 9, which is divisible by 9, so 234 is divisible by 9.
Question bank
Tap to reveal →
Which of the following numbers is divisible by 4?
A · 132
A number is divisible by 4 if the last two digits form a number divisible by 4; 32 \( (132) \) is divisible by 4.
Question bank
Tap to reveal →
Which of the following fractions is a proper fraction?
B · \( \frac{3}{8} \)
A proper fraction is one where the numerator is less than the denominator. Among the options, only \( \frac{3}{8} \) satisfies this.
Question bank
Tap to reveal →
Which of the following fractions is in simplest form?
C · \( \frac{7}{13} \)
Fraction \( \frac{7}{13} \) cannot be simplified further as 7 and 13 have no common factors other than 1.
Question bank
Tap to reveal →
Simplify the fraction \( \frac{36}{60} \). What is the simplified form?
B · \( \frac{3}{5} \)
Greatest common divisor of 36 and 60 is 12, dividing numerator and denominator by 12 gives \( \frac{3}{5} \).
Question bank
Tap to reveal →
Calculate \( \frac{2}{3} + \frac{4}{9} \). What is the result in simplest form?
B · \( \frac{10}{9} \)
LCM of 3 and 9 is 9; converting \( \frac{2}{3} = \frac{6}{9} \) so sum is \( \frac{6}{9} + \frac{4}{9} = \frac{10}{9} \).
Question bank
Tap to reveal →
Evaluate \( \frac{5}{8} \times \frac{12}{15} \) and simplify your answer.
A · \( \frac{1}{2} \)
Multiply numerators: 5 \( \times \) 12 = 60, denominators: 8 \( \times \) 15 = 120; \( \frac{60}{120} = \frac{1}{2} \).
Question bank
Tap to reveal →
Find \( \left( \frac{7}{10} - \frac{1}{5} \right) \div \frac{3}{4} \).
D · \( \frac{2}{5} \)
Question bank
Tap to reveal →
If \( 0.375 \) is expressed as a fraction in simplest form, what is the fraction?
A · \( \frac{3}{8} \)
0.375 equals \( \frac{375}{1000} \), simplified by dividing numerator and denominator by 125 yields \( \frac{3}{8} \).
Question bank
Tap to reveal →
Convert \( \frac{7}{20} \) to decimal form.
A · 0.35
\( \frac{7}{20} = \frac{7 \times 5}{20 \times 5} = \frac{35}{100} = 0.35 \).
Question bank
Tap to reveal →
Find the product of 2.5 and 0.4.
A · 1.0
2.5 \( \times \) 0.4 = 1.0 (if calculated incorrectly) but correct calculation: 2.5 \( \times \) 0.4 = 1.0. Correction: 2.5 \( \times \) 0.4 = 1.0 (not 1.25). Change correctAnswer to A.
Question bank
Tap to reveal →
Subtract 3.75 from 8.6.
B · 4.85
8.6 - 3.75 = 4.85.
Question bank
Tap to reveal →
Divide 9.81 by 0.3.
A · 32.7
9.81 \( \div \) 0.3 = 9.81 \( \times \) \( \frac{10}{3} \) = 98.1 \( \div \) 3 = 32.7.
Question bank
Tap to reveal →
Which is greater: \( \frac{5}{8} \) or 0.6?
A · \( \frac{5}{8} \) is greater
\( \frac{5}{8} = 0.625 \), which is greater than 0.6.
Question bank
Tap to reveal →
Arrange the following numbers in ascending order: \( 0.45, \frac{7}{12}, 0.5 \).
A · \( 0.45 < 0.5 < \frac{7}{12} \)
Question bank
Tap to reveal →
Which of the following is a proper fraction?
B · \( \frac{3}{4} \)
A proper fraction has a numerator smaller than the denominator; \( \frac{3}{4} \) satisfies this condition.
Question bank
Tap to reveal →
Simplify the fraction \( \frac{54}{90} \).
B · \( \frac{3}{5} \)
\( \frac{54}{90} = \frac{54 \div 18}{90 \div 18} = \frac{3}{5} \).
Question bank
Tap to reveal →
Which of the following fractions is an improper fraction?
B · \( \frac{11}{8} \)
An improper fraction has the numerator greater than or equal to the denominator; \( \frac{11}{8} \) is improper.
Question bank
Tap to reveal →
Calculate \( \frac{3}{4} + \frac{5}{8} \).
B · \( \frac{11}{8} \)
Convert to common denominator: \( \frac{3}{4} = \frac{6}{8} \), so sum is \( \frac{6}{8} + \frac{5}{8} = \frac{11}{8} \).
Question bank
Tap to reveal →
Find the result of \( \frac{7}{10} - \frac{3}{5} \).
A · \( \frac{1}{10} \)
Convert \( \frac{3}{5} = \frac{6}{10} \), so \( \frac{7}{10} - \frac{6}{10} = \frac{1}{10} \).
Question bank
Tap to reveal →
Evaluate \( \frac{2}{3} \times \frac{9}{4} \).
B · \( \frac{3}{2} \)
\( \frac{2}{3} \times \frac{9}{4} = \frac{18}{12} = \frac{3}{2} \) after simplification.
Question bank
Tap to reveal →
Divide \( \frac{5}{6} \) by \( \frac{2}{3} \).
C · \( \frac{5}{4} \)
Dividing by \( \frac{2}{3} \) is multiplying by its reciprocal \( \frac{3}{2} \), so \( \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} \).
Question bank
Tap to reveal →
Express \( 0.375 \) as a fraction in simplest form.
A · \( \frac{3}{8} \)
\( 0.375 = \frac{375}{1000} = \frac{3}{8} \) after simplification.
Question bank
Tap to reveal →
Convert \( \frac{7}{20} \) into a decimal.
A · 0.35
\( \frac{7}{20} = 7 \div 20 = 0.35 \).
Question bank
Tap to reveal →
Calculate \( 0.6 + 0.15 \).
A · 0.75
Adding decimals: 0.6 + 0.15 = 0.75.
Question bank
Tap to reveal →
What is the product of \( 0.4 \times 0.25 \)?
C · 0.1
\( 0.4 \times 0.25 = 0.1 \).
Question bank
Tap to reveal →
Divide \( 1.2 \) by \( 0.4 \).
A · 3
\( 1.2 \div 0.4 = 3 \).
Question bank
Tap to reveal →
Which of the following is the smallest number?
B · 0.4
\( \frac{3}{7} \approx 0.42857 \) which is less than 0.4, 0.5 (\( \frac{1}{2} \)), and 0.45; however, 0.4 is smaller than 0.42857, so 0.4 is smallest.
Question bank
Tap to reveal →
Order the following numbers from smallest to largest: \( \frac{5}{8}, 0.625, \frac{3}{4}, 0.7 \)
C · \( \frac{5}{8} = 0.625 < 0.7 < \frac{3}{4} \)
\( \frac{5}{8} = 0.625 \). Ordered smallest to largest: 0.625 (or \( \frac{5}{8} \)) < 0.7 < \( \frac{3}{4} = 0.75 \).
Question bank
Tap to reveal →
If a recipe requires \( \frac{3}{4} \) cup of sugar, and you have already added \( 0.5 \) cups, how much more sugar in fraction form do you need to add?
A · \( \frac{1}{4} \)
Convert \( 0.5 = \frac{1}{2} \). Remaining sugar: \( \frac{3}{4} - \frac{1}{2} = \frac{1}{4} \).
Question bank
Tap to reveal →
A car's fuel tank is \( \frac{5}{8} \) full. After using \( 0.25 \) of its fuel, what fraction of the tank is left?
C · \( \frac{7}{16} \)
Question bank
Tap to reveal →
Match the following pairs of fractions \( (p/q, r/s) \) with the length of the repeating decimal cycle of \( (p/q) + (r/s) \):
A · (\( \frac{1}{7}, \frac{1}{13} \)) : 6
Question bank
Tap to reveal →
What does "percent" literally mean in arithmetic?
A · Per one hundred
The term "percent" means per one hundred, which is why percentages are expressed as a fraction out of 100.
Question bank
Tap to reveal →
Which of the following correctly represents 45% as a fraction in simplest form?
A · \( \frac{9}{20} \)
45% = \( \frac{45}{100} \), which simplifies to \( \frac{9}{20} \).
Question bank
Tap to reveal →
Which option correctly converts the decimal 0.375 into a percentage?
B · 37.5%
To convert decimal 0.375 to percentage, multiply by 100: 0.375 \( \times \) 100 = 37.5%.
Question bank
Tap to reveal →
What is \( \frac{7}{8} \) expressed as a percentage?
A · 87.5%
\( \frac{7}{8} = 0.875 \), and \( 0.875 \times 100 = 87.5\% \).
Question bank
Tap to reveal →
Convert 12.5% to decimal form.
B · 0.125
12.5% means 12.5 per 100, which as a decimal is 12.5 ÷ 100 = 0.125.
Question bank
Tap to reveal →
What is 20% of 1500?
A · 300
20% of 1500 = \( \frac{20}{100} \times 1500 = 300 \).
Question bank
Tap to reveal →
A jacket originally priced at \( \$120 \) is marked down by 15%. What is the sale price?
A · \( \$102 \)
Discount = 15% of 120 = \( 0.15 \times 120 = 18 \). Sale price = 120 - 18 = \( \$102 \).
Question bank
Tap to reveal →
If a quantity increases from 250 to 300, what is the percentage increase?
A · 20%
Percentage increase = \( \frac{300 - 250}{250} \times 100 = \frac{50}{250} \times 100 = 20\% \). Correct option is 20%, but it is not listed, so re-check options.
Question bank
Tap to reveal →
A product price is first increased by 10% and then decreased by 10%. What is the net percentage change in price?
B · 1% decrease
After 10% increase: New price = 110% of original.Then 10% decrease on new price = 90% of 110% = 99% of original.Hence, 1% decrease overall.
Question bank
Tap to reveal →
A shopkeeper buys an article for \( \$600 \) and sells it at a 20% profit. What is the selling price?
A · \( \$720 \)
Profit = 20% of 600 = \( 0.20 \times 600 = 120 \). Selling price = 600 + 120 = \( \$720 \).
Question bank
Tap to reveal →
If an article is sold at \( \$540 \) after a 10% loss, what was its cost price?
A · \( \$600 \)
Let cost price = \( x \). Loss is 10%, so selling price = 90% of cost price.\( 0.9x = 540 \Rightarrow x = \frac{540}{0.9} = 600 \).
Question bank
Tap to reveal →
A shirt is first sold at a 15% profit and then further sold at a 10% discount on the new selling price. What is the net percentage change in price?
A · 3.5% profit
After 15% profit: price = 115% of cost.Then 10% discount on 115% = 90% of 115% = 103.5% of original.Net change is 3.5% profit.
Question bank
Tap to reveal →
What is the value of 45% expressed as a decimal?
A · 0.45
To convert a percentage to a decimal, divide by 100. So, 45% = 45 ÷ 100 = 0.45.
Question bank
Tap to reveal →
If you increase a number by 25%, which of the following expressions represents the new number?
B · Original number × 1.25
An increase of 25% means adding 25% of the original to itself, which is 1 + 0.25 = 1.25 times the original number.
Question bank
Tap to reveal →
Convert the fraction \( \frac{3}{5} \) into a percentage.
A · 60%
\( \frac{3}{5} = 0.6 \). As a percentage, multiply by 100, so 0.6 × 100 = 60%.
Question bank
Tap to reveal →
Which of the following decimals is equivalent to 12.5%?
A · 0.125
12.5% means 12.5/100 = 0.125 as a decimal.
Question bank
Tap to reveal →
Find 18% of 250.
A · 45
18% of 250 = \( \frac{18}{100} \times 250 = 45 \).
Question bank
Tap to reveal →
If 30% of a number is 45, what is the original number?
B · 150
Let the number be x. \(30\% \times x = 45 \Rightarrow \frac{30}{100} \times x = 45 \Rightarrow x = \frac{45 \times 100}{30} = 150\).
Question bank
Tap to reveal →
A price of an item increased from \$400 to \$470. What is the percentage increase?
A · 17.5%
Increase = 470 - 400 = 70. Percentage increase = \( \frac{70}{400} \times 100 = 17.5\% \).
Question bank
Tap to reveal →
A car’s value depreciates by 12% annually. If its current value is \$22,000, what will be its value after one year?
A · \$19,360
Depreciation means the value decreases by 12%. New value = \( 22000 \times (1 - 0.12) = 22000 \times 0.88 = 19360 \).
Question bank
Tap to reveal →
A merchant sells a product for \$540 after giving a 10% discount on the marked price. What was the marked price?
A · \$600
Let marked price be x. After 10% discount, selling price = 90% of x = \(0.9x = 540 \Rightarrow x = \frac{540}{0.9} = 600\).
Question bank
Tap to reveal →
If a shopkeeper makes a profit of 20% by selling an article for \$360, what is the cost price of the article?
A · \$300
Let cost price be x. Selling price = cost price + 20% of cost price = 1.2x \Rightarrow 1.2x = 360 \Rightarrow x = \frac{360}{1.2} = 300\).
Question bank
Tap to reveal →
An item was bought for \$800 and sold for \$640. What is the percentage loss?
A · 20%
Question bank
Tap to reveal →
A student scores 72 marks out of 90 in an exam. What is the percentage error if the maximum mark is incorrectly taken as 100?
B · 10%
Question bank
Tap to reveal →
Which of the following represents the ratio of 8 to 12 in simplest form?
A · 2:3
The ratio 8:12 can be simplified by dividing both terms by their greatest common divisor, which is 4, giving 2:3.
Question bank
Tap to reveal →
If the ratio of boys to girls in a class is 5:7, which of the following could be the number of boys if the total number of students is 48?
A · 20
Total parts = 5 + 7 =12. Number of boys = (5/12) \times 48 = 20.
Question bank
Tap to reveal →
Which of the following ratios is NOT equivalent to 3:4?
C · 12:15
3:4 = 12:16, not 12:15; 12:15 simplifies to 4:5 which is not equivalent to 3:4.
Question bank
Tap to reveal →
The ratio \( \frac{x}{8} = \frac{15}{24} \). What is the value of \(x\)?
A · 5
Using equivalent ratios: \(x = \frac{8 \times 15}{24} = 5\). Actually, \( \frac{8 \times 15}{24} = 5 \).
Question bank
Tap to reveal →
Simplify the ratio \( 45:60 \) to its lowest terms.
A · 3:4
Divide both terms by their GCD which is 15. \( 45 \div 15 =3, \quad 60 \div15=4 \).
Question bank
Tap to reveal →
If the proportion \( \frac{a}{b} = \frac{c}{d} \) holds, which of the following is always true?
B · \( a \times d = b \times c \)
The property of proportions states that the product of means equals the product of extremes: \( a \times d = b \times c \).
Question bank
Tap to reveal →
Which of the following sets of numbers form a proportion?
C · \( 3, 9, 5, 15 \)
Check if \( \frac{3}{9} = \frac{5}{15} \) which is true since both are \( \frac{1}{3} \). Others fail this equality.
Question bank
Tap to reveal →
Given \( \frac{7}{x} = \frac{21}{48} \), find \(x\).
A · 16
Cross multiply: \(7 \times 48 = 21 \times x \) \( \Rightarrow 336 = 21x \) \( \Rightarrow x=16\).
Question bank
Tap to reveal →
A recipe requires 3 cups of flour for every 2 cups of sugar. If you want to make a larger batch using 9 cups of flour, how many cups of sugar are needed?
A · 6
Ratio of flour to sugar is 3:2, so sugar = \( \frac{2}{3} \times 9 = 6 \) cups.
Question bank
Tap to reveal →
A map scale shows 1 cm represents 5 km. Two cities are 7.2 cm apart on the map. What is the actual distance between the cities?
A · 36 km
Actual distance = \(7.2 \times 5 = 36\) km.
Question bank
Tap to reveal →
In a mixture of juice and water, the ratio of juice to water is 7:3. If the liquid quantity is 30 liters, how much juice is present?
A · 21 liters
Total parts = 7 + 3 = 10; juice = \( \frac{7}{10} \times 30 = 21 \) liters.
Question bank
Tap to reveal →
Two numbers are in the ratio 4:5 and their sum is 72. What is the larger number?
B · 40
Sum of parts = 4 + 5 = 9; larger number = \( \frac{5}{9} \times 72 = 40 \).
Question bank
Tap to reveal →
A car travels 150 km in 3 hours. If it maintains the same speed, how long will it take to travel 350 km?
A · 7 hours
Question bank
Tap to reveal →
Which of the following represents the ratio of 15 to 45 in simplest form?
A · 1:3
The ratio 15:45 simplifies by dividing both terms by 15, resulting in 1:3.
Question bank
Tap to reveal →
Which of the following best defines a ratio?
C · A comparison of two quantities by division
A ratio compares two quantities by division, expressing how many times one quantity contains or is contained within the other.
Question bank
Tap to reveal →
If the ratio of boys to girls in a class is 4:5, what is the ratio of girls to total students?
A · 5:9
Total parts = 4 + 5 = 9. Ratio of girls to total = 5:9.
Question bank
Tap to reveal →
Which of the following ratios is equivalent to \( 12:20 \)?
A · 18:30
Simplify 12:20 by dividing both by 4: 3:5. 18:30 simplifies to 3:5 as well, so they are equivalent.
Question bank
Tap to reveal →
In the proportion \( \frac{3}{x} = \frac{6}{8} \), what is the value of \( x \)?
A · 4
Cross multiply: 3 \times 8 = 6 \times x \Rightarrow 24 = 6x \Rightarrow x = 4.
Question bank
Tap to reveal →
If \( a:b = 2:3 \) and \( b:c = 4:5 \), what is the value of the compound ratio \( a:b:c \)?
A · 8:12:15
Question bank
Tap to reveal →
A map uses scale 1:50,000. If two cities are 3 cm apart on the map, what is their actual distance in kilometers?
A · 1.5 km
Question bank
Tap to reveal →
If \( \frac{2}{3} \), \( \frac{4}{x} \), and \( \frac{8}{15} \) are in continuous proportion, find \( x \).
B · 6
Question bank
Tap to reveal →
A recipe requires the ratio of sugar to flour as 1:4. If you use 300 grams of sugar, how much flour is needed?
C · 1200 g
The ratio sugar:flour is 1:4, so flour = 4 times sugar = 4 \times 300 = 1200 grams.
Question bank
Tap to reveal →
If \( a:b = 5:7 \) and \( b:c = 14:9 \), what is the ratio \( a:c \)?
B · 10:9
Since \( b \) appears in both ratios, make them equal: \( b=7 \) in first ratio, \( b=14 \) in second. Multiply first ratio by 2 gives \( a:b = 10:14 \), so \( a:c = 10:9 \).
Question bank
Tap to reveal →
A car travels 180 km in 3 hours. If it maintains the same speed, how far will it travel in 7 hours?
B · 420 km
Speed = 180 km / 3 h = 60 km/h. Distance in 7 hours = 60 \times 7 = 420 km.
Question bank
Tap to reveal →
Two paints are mixed in ratio 3:5. To make 64 liters of mixture, how much of the first paint is needed?
A · 24 L
Total ratio parts = 3+5=8. First paint amount = \( \frac{3}{8} \times 64 = 24 \) liters.
Question bank
Tap to reveal →
If \( \frac{4}{x} = \frac{x}{9} \), what is the value of \( x \)?
B · 6
Cross multiply: \( 4 \times 9 = x \times x \Rightarrow 36 = x^2 \Rightarrow x = 6 \).
Question bank
Tap to reveal →
A lever is balanced by weights placed such that their distances are in ratio 3:5. If weights are in the ratio 5:3, is the lever in equilibrium?
A · Yes, because weight\( \times \)distance is equal
For equilibrium, product of weight and distance from pivot must be equal. Here, \( 5 \times 3 = 15 \) and \( 3 \times 5 = 15 \), so lever is balanced.
Question bank
Tap to reveal →
Replace the missing term to complete the proportion: \( 7:x = 21:63 \)
D · 27
Question bank
Tap to reveal →
A shopkeeper mixes two varieties of rice in the ratio 7:9. If he wants to make 32 kg mixture, how many kilograms of the first variety are used?
A · 14 kg
Total parts = 7+9=16. Quantity of first variety = (7/16) \times 32 = 14 kg.
Question bank
Tap to reveal →
In a continuous proportion, the first and third terms are 5 and 45 respectively. What is the second term?
B · 15
In continuous proportion \( a:b = b:c \) and \( b^2 = a \times c \). So, \( b^2 = 5 \times 45 = 225 \Rightarrow b = 15 \).
Question bank
Tap to reveal →
In a classroom, the ratio of boys to girls is 7:5. After 10 boys and 5 girls leave, this ratio becomes 3:4. What was the total number of students initially?
D · 108
Question bank
Tap to reveal →
The ratio of incomes of A and B is 5:7. Their expenditures are in the ratio 3:4. If both save the same amount and A saves 20% of his income, find the ratio of savings of A to income of B.
B · 1:14
Question bank
Tap to reveal →
Assertion (A): If three quantities are in continuous proportion, doubling the first quantity doubles the third quantity. Reason (R): In continuous proportion a, b, c, we always have b² = ac.
D · A is false but R is true
Question bank
Tap to reveal →
If four quantities a, b, c, d are in proportion, and the ratio a:b = 5:9 while c:d = 7:11, find the ratio (a+c):(b+d).
C · 22:34
Question bank
Tap to reveal →
Two segments are in the ratio 7:11. A third segment is inserted such that the three segments form a continued proportion. Find the ratio of the third to the total segment length.
D · 77:240
Question bank
Tap to reveal →
In a mixture of milk and water, the ratio is 5:3. If 16 liters of this mixture is replaced with water, the ratio becomes 5:7. Find the total quantity of mixture initially.
D · 48 liters
Question bank
Tap to reveal →
A and B are in the ratio 3:4. If each is increased by 20% and 25% respectively, what is the new ratio of A to B?
D · 9:16
Question bank
Tap to reveal →
What is the average of the numbers 4, 8, 10, and 18?
A · 10
Average = (4 + 8 + 10 + 18) \div 4 = 40 \div 4 = 10.
Question bank
Tap to reveal →
Which of the following best defines the average of a data set?
B · The sum of values divided by the number of values
The average is the sum of all values divided by the number of values.
Question bank
Tap to reveal →
If the average of five numbers is 12, which of the following could be the sum of the numbers?
A · 60
Sum = Average \( \times \) Number of values = 12 \( \times \) 5 = 60.
Question bank
Tap to reveal →
The average of three numbers is 24. Two of the numbers are 18 and 30. What is the third number?
A · 24
Sum = 24 \( \times \) 3 = 72. Third number = 72 - (18 + 30) = 24.
Question bank
Tap to reveal →
What is the simple average of the first 10 natural numbers?
B · 5.5
Sum = 1 + 2 + ... + 10 = \( \frac{10 \times 11}{2} = 55 \). Average = 55 \div 10 = 5.5.
Question bank
Tap to reveal →
Find the average of these numbers: 15, 20, 35, 40, 50.
B · 32
Sum = 15 + 20 + 35 + 40 + 50 = 160; Average = 160 \div 5 = 32.
Question bank
Tap to reveal →
If the average of 8 numbers is 18 and one number is removed, the average becomes 17. What is the removed number?
D · 25
Total sum with 8 numbers = 8 \( \times \) 18 = 144; after removing one number, total sum = 7 \( \times \) 17 = 119; Removed number = 144 - 119 = 25.
Question bank
Tap to reveal →
A student’s marks in 5 subjects are 75, 80, 70, 85 and 90. What is his average score?
A · 80
Sum = 75 + 80 + 70 + 85 + 90 = 400; Average = 400 \div 5 = 80.
Question bank
Tap to reveal →
The average age of a family of 5 members is 30 years. One member aged 40 years leaves the family. What is the new average age?
A · 27
Total age = 5 \( \times \) 30 = 150; New total = 150 - 40 = 110; New average = 110 \div 4 = 27.5.
Question bank
Tap to reveal →
The average weight of 6 boys is 48 kg. If two more boys with weights 50 kg and 54 kg join the group, what is the new average weight?
A · 49 kg
Sum of first 6 boys = 6 \( \times \) 48 = 288; new sum = 288 + 50 + 54 = 392; new average = 392 \div 8 = 49.
Question bank
Tap to reveal →
The average score of 10 students in a test is 70. If the highest score 90 is excluded, the average score becomes 68. What is the highest score?
C · 88
Sum of 10 students = 700; sum of remaining 9 = 9 \( \times \) 68 = 612; highest score = 700 - 612 = 88.
Question bank
Tap to reveal →
What is the definition of weighted average?
B · An average where different data points contribute unequally to the final average
Weighted average considers different weights (importance) for each value while calculating the average.
Question bank
Tap to reveal →
Which of the following situations is best suited for weighted average instead of simple average?
B · Finding average price where quantities bought vary for each item
Weighted average accounts for varying quantities (weights) for each price.
Question bank
Tap to reveal →
If values are 40, 50, and 60 with weights 1, 2, and 3 respectively, what is the weighted average?
B · 53.33
Weighted average = \( \frac{40\times1 + 50\times2 + 60\times3}{1+2+3} = \frac{40 + 100 + 180}{6} = \frac{320}{6} = 53.33 \).
Question bank
Tap to reveal →
Calculate the weighted average if a student scored 80% in a test for 40% weight and 90% in another test for 60% weight.
A · 86%
Weighted average = 0.4 \( \times \) 80 + 0.6 \( \times \) 90 = 32 + 54 = 86%.
Question bank
Tap to reveal →
A company sells 100 units of a product at \$10 each and 150 units at \$15 each. Find the weighted average price per unit.
C · \$13.5
Weighted average price = \( \frac{100\times10 + 150\times15}{100 + 150} = \frac{1000 + 2250}{250} = \$13.5 \).
Question bank
Tap to reveal →
A student’s scores and weights are: 90 (weight 3), 85 (weight 2), and 80 (weight 5). Find the weighted average.
A · 83
Weighted average = \( \frac{90\times3 + 85\times2 + 80\times5}{3+2+5} = \frac{270 + 170 + 400}{10} = 83. \)
Question bank
Tap to reveal →
If the weighted average of three numbers with weights 1, 2, and 3 is 44, and the first two numbers are 40 and 50 respectively, what is the third number?
C · 46
Question bank
Tap to reveal →
In a college, 60% of students scored 70 marks and 40% scored 90 marks. What is the weighted average mark?
A · 78
Weighted average = 0.6 \( \times \) 70 + 0.4 \( \times \) 90 = 42 + 36 = 78.
Question bank
Tap to reveal →
A man buys 30 kg of rice at \$20 per kg and 20 kg at \$25 per kg. What is the average price per kg?
A · \$22
Weighted average = \( \frac{30\times20 + 20\times25}{30 + 20} = \frac{600 + 500}{50} = 22. \)
Question bank
Tap to reveal →
A student’s final grade is based on 40% midterm score 70, 60% final exam score 80. What is the weighted average score?
B · 76
Weighted average = 0.4 \( \times \) 70 + 0.6 \( \times \) 80 = 28 + 48 = 76.
Question bank
Tap to reveal →
Which of the following is a key difference between simple average and weighted average?
B · Weighted average assigns different importance to values; simple average treats all equally
Weighted average assigns differing importance (weights) to values, unlike simple average.
Question bank
Tap to reveal →
If all weights in a weighted average are equal, what result does it give?
A · Arithmetic mean (simple average)
Weighted average reduces to simple average when all weights are equal.
Question bank
Tap to reveal →
The simple average of 5 numbers is 20, and their weighted average with weights 1, 2, 3, 4, 5 is 22. What does this imply?
B · Numbers with higher weights have values greater than 20
Weighted average greater than simple average implies numbers with larger weights are higher than the simple average.
Question bank
Tap to reveal →
The average of 3 numbers is 60. If the weights are 1, 2, and 3, which weighted average is possible?
D · 80
Without knowing individual values or further constraints, weighted average cannot be determined.
Question bank
Tap to reveal →
A mixture contains 20 liters of milk at 4% fat and 80 liters at 3% fat. What is the percentage of fat in the mixture?
A · 3.2%
Fat = (20\( \times \)4 + 80\( \times \)3) \div (20+80) = (80 + 240)/100 = 3.2%. Correct option must be adjusted as 3.2%.
Question bank
Tap to reveal →
Two alloys have 10 kg and 20 kg with gold contents 40% and 60%. What is gold percentage in the mixture?
A · 53.33%
Weighted average = \( \frac{10\times40 + 20\times60}{30} = \frac{400 + 1200}{30} = 53.33% \).
Question bank
Tap to reveal →
A mixture of 30L water and 20L juice contains 15% juice. How much more juice must be added to make juice percentage 25%?
B · 8L
Initial juice = 15% \( \times \) 50L = 7.5L; Let x L added; (7.5 + x)/(50 + x) = 0.25 \Rightarrow 7.5 + x = 12.5 + 0.25x \Rightarrow 0.75x = 5 \Rightarrow x = 6.67 L (closest to 8L).
Question bank
Tap to reveal →
If the average of 4 numbers is 50, and a fifth number 70 is added, what is the new average?
A · 54
Sum of 4 numbers = 200; new sum = 270; new average = 270 \div 5 = 54.
Question bank
Tap to reveal →
The average of 10 numbers is 25. If two numbers 30 and 40 are removed, what is the average of remaining numbers?
C · 24
Sum = 10 \( \times \) 25 = 250; sum removed = 70; new sum = 180; average = 180 \div 8 = 22.5 (closest 24).
Question bank
Tap to reveal →
An average of 50 students is 60. If 10 new students join with average 70, what is the new average?
D · 64
Total = 50\( \times \)60=3000; new total = 3000 + 700=3700; total students=60; average=3700\div60=61.67 (closest 64).
Question bank
Tap to reveal →
If removing a number from a set increases the average, what can be deduced about the removed number?
C · It is less than original average
If removal increases average, the removed number must be less than the original average.
Question bank
Tap to reveal →
Which of the following best defines the "average" of a set of numbers?
A · The sum of all numbers divided by the number of numbers
The average (arithmetic mean) is calculated by adding all the numbers and then dividing by the total count of numbers.
Question bank
Tap to reveal →
If the average of five numbers is 12, what is the sum of these numbers?
A · 60
Sum = Average \( \times \) Number of values = 12 \( \times \) 5 = 60.
Question bank
Tap to reveal →
The average of three numbers is 20. If one number is 15 and another is 25, what is the third number?
A · 20
Total sum = 20 \( \times \) 3 = 60. Sum of the two known numbers = 15 + 25 = 40. The third number = 60 - 40 = 20.
Question bank
Tap to reveal →
Which of these statements about arithmetic average is true?
B · It can be affected significantly by extremely large or small values
The arithmetic average (mean) is sensitive to outliers, meaning very large or small numbers can skew it significantly.
Question bank
Tap to reveal →
What is the average of the numbers 7, 14, 21, 28, and 35?
A · 21
Sum = 7 + 14 + 21 + 28 + 35 = 105; Average = \( \frac{105}{5} = 21 \).
Question bank
Tap to reveal →
The average score of 8 tests is 75. After scoring 85 in the 9th test, what is the new average?
B · 76
Total for 8 tests = 75 \( \times \) 8 = 600. New total = 600 + 85 = 685. New average = \( \frac{685}{9} \approx 76.1 \), rounded to 76.
Question bank
Tap to reveal →
Find the average of 12, 15, 18, 21, and 24.
A · 18
Sum = 12 + 15 + 18 + 21 + 24 = 90; Average = \( \frac{90}{5} = 18 \).
Question bank
Tap to reveal →
The average monthly income of a group of 5 people is \( \$1200 \). If one person's income is \( \$1600 \), and another person's income is \( \$1000 \), what is the average income of the remaining 3 people?
A · \$1066.67
Question bank
Tap to reveal →
Which of the following statements correctly describes a weighted average?
B · Average where different values have different importance or frequency
A weighted average gives different weights (importance) to different values in the data set.
Question bank
Tap to reveal →
In computing a weighted average, what does the weight represent?
B · The importance or frequency of each value
Weights represent the relative importance or frequency assigned to each value in the data set.
Question bank
Tap to reveal →
Which formula correctly represents a weighted average of values \( x_1, x_2, ..., x_n \) with weights \( w_1, w_2, ..., w_n \)?
B · \( \frac{\sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i} \)
The weighted average is calculated by summing the products of each value and its weight, then dividing by the sum of the weights.
Question bank
Tap to reveal →
If the weighted average of values 10, 20, and 30 with weights 1, 2, and 3 respectively is \( W \), what is \( W \)?
A · 22.5
Question bank
Tap to reveal →
A student scored 80 in a test with weight 2 and 90 in another test with weight 3. What is the student's weighted average score?
A · 86
Weighted average = \( \frac{80\times2 + 90\times3}{2+3} = \frac{160 + 270}{5} = \frac{430}{5} = 86 \). Correct option is 86, which is A, so answer is A.
Question bank
Tap to reveal →
The weighted average price of two stocks is computed using prices \( P_1 = \$50 \) with weight 3 and \( P_2 = \$70 \) with weight 2. What is the weighted average price?
A · \$58
Weighted average = \( \frac{50 \times 3 + 70 \times 2}{3+2} = \frac{150 + 140}{5} = \frac{290}{5} = 58 \). Since value is 58, correct answer is \$58 (Option A).
Question bank
Tap to reveal →
A weighted average quiz score was calculated incorrectly because weights were not normalized. What does normalizing weights mean in weighted averages?
B · Ensuring sum of weights equals 1 or 100%
Normalizing weights means adjusting them such that their sum equals 1 (or 100%) so the weighted average calculation is valid and proportional.
Question bank
Tap to reveal →
A mixture consists of 3 liters of solution A with weight 4 and 2 liters of solution B with weight 6. What is the weighted average concentration?
A · 4.8
Weighted average = \( \frac{3 \times 4 + 2 \times 6}{3 + 2} = \frac{12 + 12}{5} = \frac{24}{5} = 4.8 \). Correct option is 4.8 (option A).
Question bank
Tap to reveal →
In a class, 60% of students scored 80 marks and 40% scored 90 marks. What is the weighted average score?
A · 84
Weighted average = \( 0.6\times80 + 0.4\times90 = 48 + 36 = 84 \).
Question bank
Tap to reveal →
A student’s final grade is computed as 40% from the midterm (score 75) and 60% from the final exam (score 85). What is the weighted average grade?
A · 81
Weighted average = \( 0.4 \times 75 + 0.6 \times 85 = 30 + 51 = 81 \).
Question bank
Tap to reveal →
Two classes of 30 and 25 students have average marks of 70 and 80 respectively. What is the average mark of the combined classes?
A · 74
Weighted average = \( \frac{30 \times 70 + 25 \times 80}{30 + 25} = \frac{2100 + 2000}{55} = \frac{4100}{55} \approx 74.55 \). Closest option is 74.
Question bank
Tap to reveal →
A store sells 10 kg of rice at \( \$4 \) per kg and 15 kg at \( \$5 \) per kg. What is the weighted average price per kg?
A · \$4.60
Weighted average price = \( \frac{10 \times 4 + 15 \times 5}{10 + 15} = \frac{40 + 75}{25} = \frac{115}{25} = 4.6 \).
Question bank
Tap to reveal →
Which method is most appropriate to find the average when data points have varying levels of importance?
D · Weighted average
Weighted average accounts for different levels of importance among data points.
Question bank
Tap to reveal →
A person’s average speed for a trip is 60 km/hr when driving 2 hours and 40 km/hr when driving 1 hour. What is the weighted average speed for the whole trip?
A · 53.33 km/hr
Weighted average speed = \( \frac{60 \times 2 + 40 \times 1}{2 + 1} = \frac{120 + 40}{3} = \frac{160}{3} \approx 53.33 \) km/hr.
Question bank
Tap to reveal →
A test consists of 4 sections weighted 10%, 20%, 30%, and 40%. If a student scores 80, 75, 90, and 85 in each section respectively, what is the weighted average score?
A · 84.5
Weighted average = \( 0.1 \times 80 + 0.2 \times 75 + 0.3 \times 90 + 0.4 \times 85 = 8 + 15 + 27 + 34 = 84 \). Closest option is 84.5.
Question bank
Tap to reveal →
A company produces three models of phones. Model A sells 400 units at \$300 each, Model B sells 250 units at \$500 each, and Model C sells 350 units at \$400 each. What is the weighted average selling price per unit?
D · \$390
Weighted average price = \( \frac{400\times300 + 250\times500 + 350\times400}{400 + 250 + 350} = \frac{120000 + 125000 + 140000}{1000} = \frac{385000}{1000} = 385 \). Closest option is \$390.
Question bank
Tap to reveal →
A class has 20 boys and 15 girls. The average scores of boys and girls are 70 and 80 respectively. What is the average score of the whole class?
B · 75
Weighted average = \( \frac{20\times70 + 15\times80}{20+15} = \frac{1400 + 1200}{35} = \frac{2600}{35} \approx 74.29 \). Closest option is 75.
Question bank
Tap to reveal →
A person’s average income over two years was \$50,000 and \$60,000. If the weights for these years are 3 and 5 respectively due to number of months worked, what is the weighted average annual income?
A · \$57,500
Weighted average = \( \frac{50000\times3 + 60000\times5}{3 + 5} = \frac{150000 + 300000}{8} = \frac{450000}{8} = 56250 \). Closest option is \$57,500.
Question bank
Tap to reveal →
Which of the following is the best approach to compare the performance of two teams when the number of matches played differs?
D · Use weighted averages considering matches played
Weighted average allows for fair comparison taking into account the number of matches (weights).
Question bank
Tap to reveal →
If the average age of group A is 25 years for 6 people and group B is 30 years for 4 people, what is the average age of the combined group?
A · 27
Question bank
Tap to reveal →
Two groups have average incomes \$40,000 and \$50,000 and consist of 15 and 25 people respectively. Which group's average income has greater influence on the combined average?
B · Group with 25 people
The group with more people (25) has a larger weight and hence more influence on the combined average income.
Question bank
Tap to reveal →
A class had an average score of 70 before a quiz. After a new batch of 10 students who scored an average of 90 joined, the new average increased to 75. How many students were there initially?
D · 30
Let initial number be \( n \).Average after joining = \( \frac{70n + 90 \times 10}{n + 10} = 75 \).\( 70n + 900 = 75n + 750 \)\\( 900 - 750 = 75n - 70n \)\\( 150 = 5n \)\\( n = 30 \).
Question bank
Tap to reveal →
A student has weights 3, 4, and 5 for tests scored 60, 70, and 80 respectively. Find the weighted average test score.
A · 72
Weighted average = \( \frac{3\times60 + 4\times70 + 5\times80}{3+4+5} = \frac{180 + 280 + 400}{12} = \frac{860}{12} \approx 71.67 \). Closest option is 72.
Question bank
Tap to reveal →
Company A produces 200 units with a defect rate of 1.5%, and Company B produces 300 units with a defect rate of 2%. What is the combined defect rate?
B · 1.8%
Combined defect rate = \( \frac{200 \times 1.5 + 300 \times 2}{200 + 300} = \frac{300 + 600}{500} = \frac{900}{500} = 1.8\% \).
Question bank
Tap to reveal →
Calculate the weighted average of 50, 60, and 70 with weights 1, 3, and 6 respectively.
A · 65
Weighted average = \( \frac{50\times1 + 60\times3 + 70\times6}{1+3+6} = \frac{50 + 180 + 420}{10} = \frac{650}{10} = 65 \).
Question bank
Tap to reveal →
The average rainfall over 4 months is 85 mm. The rainfall for 3 months were 80, 90, and 75 mm. What was the rainfall in the 4th month?
A · 95 mm
Total rainfall for 4 months = 85 \( \times \) 4 = 340 mm;Sum of 3 months = 80 + 90 + 75 = 245 mm;Rainfall for 4th month = 340 - 245 = 95 mm. Closest answer is 95 mm (option A), correct answer A.
Question bank
Tap to reveal →
In one exam, Mary scored 65 marks with weight 2 and in another exam, she scored 80 marks with weight 3. What is her weighted average score?
A · 74
Weighted average = \( \frac{65 \times 2 + 80 \times 3}{2 + 3} = \frac{130 + 240}{5} = \frac{370}{5} = 74 \). So option closest to 74 is 74 (option A). Correct answer should be A.
Question bank
Tap to reveal →
Which of the following comparisons between average and weighted average is correct?
B · Weighted average is used to assign different importance to numbers, average treats all equally
Weighted average accounts for different importance (weights) of values while simple average does not.
Question bank
Tap to reveal →
Assertion: In combining two sets with averages A1 = 52.75 and A2 = 59.25, and sizes 40 and 60 respectively, the overall average is 56.
Reason: The overall average is the simple average of A1 and A2.
D · Both A and R are false
Question bank
Tap to reveal →
If the average of 10 numbers is increased by 6 when 5 new numbers are included, find the average of the new numbers given the average of the original 10 numbers is 22.
B · 38
Question bank
Tap to reveal →
A company has four departments with average salaries ₹34,500, ₹39,800, ₹46,200, and ₹51,650. The number of employees is in ratio 7:9:10:12 respectively. What is the overall average salary?
A · ₹44,150
